Saul Rappaport

A new technique for calculations of binary stellar evolution, with application to magnetic braking

We present a new computational technique for the study of the evolution of compact binary stellar systems with mass-losing secondaries whose masses can range between approx.0.01 M/sub sun/ and approx.1 M/sub sun/. In this technique, we utilize a composite polytrope with indices n = 3 and n = 3/2 to represent the structure of the radiative core and convective envelope, respectively. All other relevant aspects of the binary stellar evolution are calculated in detail. The advantages of this technique include (i) computational speed (more than an order of magnitude faster than more conventional binary stellar evolution codes), (ii) simplicity, which enables a more straightforward interpretation of the results in terms of the essential physics of the problem, and (iii) the generation of semianalytic expressions for the mass transfer rate and the behavior of the secondary star.

EVOLUTIONARY SEQUENCES FOR LOW- AND INTERMEDIATE-MASS X-RAY BINARIES

We present the results of a systematic study of the evolution of low- and intermediate-mass X-ray binaries (LMXBs and IMXBs). Using a standard Henyey-type stellar evolution code and a standard model for binary interactions, we have calculated 100 binary evolution sequences containing a neutron star and a normal-type companion star, where the initial mass of the secondary ranges from 0.6 to 7 M☉ and the initial orbital period from ~4 hr to ~100 days. This range samples the entire range of parameters one is likely to encounter for LMXBs and IMXBs. The sequences show an enormous variety of evolutionary histories and outcomes, where different mass transfer mechanisms dominate in different phases. Very few sequences resemble the classical evolution of cataclysmic variables, where the evolution is driven by magnetic braking and gravitational radiation alone. Many systems experience a phase of mass transfer on a thermal timescale and may briefly become detached immediately after this phase (for the more massive secondaries). In agreement with previous results (Tauris & Savonije 1999), we find that all sequences with (sub)giant donors up to ~2 M☉ are stable against dynamical mass transfer. Sequences where the secondary has a radiative envelope are stable against dynamical mass transfer for initial masses up to ~4 M☉. For higher initial masses, they experience a delayed dynamical instability after a stable phase of mass transfer lasting up to ~106 yr. Systems where the initial orbital period is just below the bifurcation period of ~18 hr evolve toward extremely short orbital periods (as short as ~10 minutes). For a 1 M☉ secondary, the initial period range that leads to the formation of ultracompact systems (with minimum periods less than ~40 minutes) is 13-18 hr. Since systems that start mass transfer in this period range are naturally produced as a result of tidal capture, this may explain the large fraction of ultracompact LMXBs observed in globular clusters. The implications of this study for our understanding of the population of X-ray binaries and the formation of millisecond pulsars are also discussed.

AN EXPLORATION OF THE PARADIGM FOR THE 2¨3 HOUR PERIOD GAP IN CATACLYSMIC VARIABLES

We critically examine the basic paradigm for the origin of the 2¨3 hr period gap in cataclysmic variables (CVs), i.e., binary systems in which a white dwarf accretes from a relatively unevolved, low-mass donor star. The observed orbital period distribution for D300 CVs shows that these systems typically have orbital periods, in the range of D80 minutes to D8 hr but a distinct dearth of systems with P orb , This latter feature of the period distribution is often referred to as the ii period gap.ˇˇ 2 [ P orb (hr) [ 3. The conventional explanation for the period gap involves a thermal bloating of the donor star for hr due to mass transfer rates that are enhanced over those that could be driven by gravitational P orb Z 3 radiation (GR) losses alone (e.g., magnetic braking). If for some reason the supplemental angular momentum losses become substantially reduced when decreases below D3 hr, the donor star will relax P orb thermally and shrink inside of its Roche lobe. This leads to a cessation of mass transfer until GR losses can bring the system into Roche lobe contact again at hr. We carry out an extensive population P orb D 2 synthesis study of CVs, starting from D3 ] 106 primordial binaries and evolving some D2 ] 104 surviving systems through their CV phase. In particular we study current-epoch distributions of CVs in the and planes, where is the mass transfer rate, q is the M5 P orb , R 2 -P orb , M 2 -P orb , q-P orb , T eff -P orb , L 2 -P orb M0 mass ratio and and are the donor star mass, radius, eUective temperature, and M 2 /M 1 , M 2 , R 2 , T eff , L 2 luminosity, respectively. This work presents a new perspective on theoretical studies of the long-term evolution of CVs. In particular, we show that if the current paradigm is correct, the secondary masses in CVs just above the period gap should be as much as D50% lower than would be inferred if one assumes a main-sequence radius-mass relation for the donor star. We quantify the relations expected M 2 -P orb from models wherein the donor stars are thermally bloated. Finally, we propose speci—c observations, involving the determination of secondary masses in CVs, that would allow for a de—nitive test of the currently accepted model (i.e., interrupted thermal bloating) for the period gap in CVs.

The evolution of highly compact binary stellar systems

A new theoretical treatment of the evolution of highly compact binary systems is presented. The evolution is calculated until almost the entire mass of the secondary has been transferred to the primary or lost from the system. It is assumed that gravitational radiation from the system is the cause of mass transfer. It is found that the structure of the mass-losing star can be approximated by an n = 3/2 polytrope, and as a result a relatively large number of different cases can be explored and some general conclusions drawn. An explanation is found for the existence of a cutoff in the orbital period distribution among the cataclysmic variables and light is shed upon the possible generic relationships among cataclysmic variables, the low-mass X-ray binaries, and the spectrally soft transient X-ray sources.

On the formation and evolution of black hole binaries

We present the results of a systematic study of the formation and evolution of binaries containing black holes and normal-star companions with a wide range of masses. We first reexamine the standard formation scenario for close black hole binaries, where the progenitor system, a binary with at least one massive component, experienced a common-envelope phase and where the spiral-in of the companion in the envelope of the massive star caused the ejection of the envelope. We estimate the formation rates for different companion masses and different assumptions about the common-envelope structure and other model parameters. We find that black hole binaries with intermediate- and high-mass secondaries can form for a wide range of assumptions, while black hole binaries with low-mass secondaries can only form with apparently unrealistic assumptions (in agreement with previous studies). We then present detailed binary evolution sequences for black hole binaries with secondaries of 2 to 17 M(circle dot) and demonstrate that in these systems the black hole can accrete appreciably even if accretion is Eddington-limited (up to 7 M(circle dot) for an initial black hole mass of 10 M(circle dot) ) and that the black holes can be spun up significantly in the process. We discuss the implications of these calculations for well-studied black hole binaries (in particular GRS 1915+105) and ultraluminous X-ray sources of which GRS 1915+105 appears to represent a typical Galactic counterpart. We also present a detailed evolutionary model for Cygnus X-1, a massive black hole binary, which suggests that at present the system is most likely in a wind mass-transfer phase following an earlier Roche-lobe overflow phase. Finally, we discuss how some of the assumptions in the standard model could be relaxed to allow the formation of low-mass, short-period black hole binaries, which appear to be very abundant in nature.

The Formation of Very Narrow Waist Bipolar Planetary Nebulae

We discuss the interaction of the slow wind blown by an asymptotic giant branch (AGB) star with a collimated fast wind (CFW) blown by its main-sequence or white dwarf companion, at orbital separations in the range of several AU a 200 AU. The CFW results from accretion of the AGB wind into an accretion disk around the companion. The fast wind is collimated by the accretion disk. We argue that such systems are the progenitors of bipolar planetary nebulae and bipolar symbiotic nebulae with a very narrow equatorial waist between the two polar lobes. The CFW wind will form two lobes along the symmetry axis and will further compress the slow wind near the equatorial plane, leading to the formation of a dense slowly expanding ring. Therefore, contrary to the common claim that a dense equatorial ring collimates the bipolar flow, we argue that in the progenitors of very narrow waist bipolar planetary nebulae, the CFW, through its interaction with the slow wind, forms the dense equatorial ring. Only later in the evolution, and after the CFW and slow wind cease, does the mass-losing star leave the AGB and blow a second, more spherical, fast wind. At this stage the flow structure becomes the one that is commonly assumed for bipolar planetary nebulae, i.e., collimation of the fast wind by the dense equatorial material. However, this results in the broadening of the waist in the equatorial plane and cannot by itself account for the presence of very narrow waists or jets. We conduct a population synthesis study of the formation of planetary nebulae in wide binary systems which quantitatively supports the proposed model. The population synthesis code follows the evolution of both stars and their arbitrarily eccentric orbit, including mass loss via stellar winds, for 5 ? 104 primordial binaries. We show the number of expected systems that blow a CFW is in accord with the number found from observations, to within the many uncertainties involved. Overall, we find that ~5% of all planetary nebulae are bipolars with very narrow waists. Our population synthesis not only supports the CFW model but more generally supports the binary model for the formation of bipolar planetary nebulae.

Evolutionary status of bright, low-mass x-ray sources/sup 1/

A model of bright, low-mass X-ray binaries is proposed which features a lower giant-branch star losing mass on a nuclear time scale to an accreting compact companion. Simple numerical models show that mass transfer rates > or =10/sup -9/ M/sub sun/ yr/sup -1/ are sustained at very nearly a constant rate until the envelope of the donor star is exhausted. The model predicts orbital periods in the range 1/sup d/-200/sup d/ and X-ray to optical luminosity ratios L/sub x//L/sub opt/roughly-equal200-1000 for these sources. It accounts in a natural way for the large fraction of the total galactic bulge luminosity emitted by a few bright (> or =10/sup 37/ ergs s/sup -1/) sources. It also accords very well with the observed X-ray and optical properties of the halo source Cyg X-2 and also with those of 2S 0921-63, provided this latter system contains a massive accreting white dwarf rather than a neutron star. Problems of the prior evolution of low-mass X-ray sources are also briefly delineated.

X-Ray and Optical Flux Ratio Anomalies in Quadruply Lensed Quasars. I. Zooming in on Quasar Emission Regions

X-ray and optical observations of quadruply lensed quasars can provide a microarcsecond probe of the lensed quasar, corresponding to scale sizes of ~102-104 gravitational radii of the central black hole. This high angular resolution is achieved by taking advantage of microlensing by stars in the lensing galaxy. In this paper we use X-ray observations of 10 lensed quasars recorded with the Chandra X-Ray Observatory as well as corresponding optical data obtained with either the Hubble Space Telescope or ground-based optical telescopes. These are analyzed in a systematic and uniform way with emphasis on the flux ratio anomalies that are found relative to the predictions of smooth lens models. A comparison of the flux ratio anomalies between the X-ray and optical bands allows us to conclude that the optical emission regions of the lensed quasars are typically larger than expected from basic thin-disk models by factors of ~3-30.

A New Class of High-Mass X-Ray Binaries: Implications for Core Collapse and Neutron Star Recoil

We investigate an interesting new class of high-mass X-ray binaries (HMXBs) with long orbital periods (Porb > 30 days) and low eccentricities (e 0.2). The orbital parameters suggest that the neutron stars in these systems did not receive a large impulse, or kick, at the time of formation. After considering the statistical significance of these new binaries, we develop a self-consistent phenomenological picture wherein the neutron stars born in the observed wide HMXBs receive only a small kick (50 km s-1), while neutron stars born in isolation, in the majority of low-mass X-ray binaries, and in many of the well-known HMXBs with Porb 30 days receive the conventional large kicks, with a mean speed of ~300 km s-1. Assuming that this basic scenario is correct, we discuss a physical process that lends support to our hypothesis, whereby the magnitude of the natal kick to a neutron star born in a binary system depends on the rotation rate of its immediate progenitor following mass transfer—the core of the initially more massive star in the binary. Specifically, the model predicts that rapidly rotating precollapse cores produce neutron stars (NSs) with relatively small kicks, and vice versa for slowly rotating cores. If the envelope of the NS progenitor is removed before it has become deeply convective, then the exposed core is likely to be a rapid rotator. However, if the progenitor becomes highly evolved prior to mass transfer, then a strong magnetic torque, generated by differential rotation between the core and the convective envelope, may cause the core to spin down to the very slow rotation rate of the envelope. Our model has important implications for the dynamics of stellar core collapse, the retention of neutron stars in globular clusters, and the formation of double neutron star systems in the Galaxy.

Possible Disintegrating Short-period Super-Mercury Orbiting KIC 12557548

We report on the discovery of stellar occultations, observed with Kepler, which recur periodically at 15.685 hr intervals, but which vary in depth from a maximum of 1.3% to a minimum that can be less than 0.2%. The star that is apparently being occulted is KIC 12557548, a V = 16 mag K dwarf with T_eff, s ≃ 4400 K. The out-of-occultation behavior shows no evidence for ellipsoidal light variations, indicating that the mass of the orbiting object is less than ~3 M_J (for an orbital period of 15.7 hr). Because the eclipse depths are highly variable, they cannot be due solely to transits of a single planet with a fixed size. We discuss but dismiss a scenario involving a binary giant planet whose mutual orbit plane precesses, bringing one of the planets into and out of a grazing transit. This scenario seems ruled out by the dynamical instability that would result from such a configuration. We also briefly consider an eclipsing binary, possibly containing an accretion disk, that either orbits KIC 12557548 in a hierarchical triple configuration or is nearby on the sky, but we find such a scenario inadequate to reproduce the observations. The much more likely explanation—but one which still requires more quantitative development—involves macroscopic particles escaping the atmosphere of a slowly disintegrating planet not much larger than Mercury in size. The particles could take the form of micron-sized pyroxene or aluminum oxide dust grains. The planetary surface is hot enough to sublimate and create a high-Z atmosphere; this atmosphere may be loaded with dust via cloud condensation or explosive volcanism. Atmospheric gas escapes the planet via a Parker-type thermal wind, dragging dust grains with it. We infer a mass-loss rate from the observations of order 1 M_⊕ Gyr^(–1), with a dust-to-gas ratio possibly of order unity. For our fiducial 0.1 M_⊕ planet (twice the mass of Mercury), the evaporation timescale may be ~0.2 Gyr. Smaller mass planets are disfavored because they evaporate still more quickly, as are larger mass planets because they have surface gravities too strong to sustain outflows with the requisite mass-loss rates. The occultation profile evinces an ingress-egress asymmetry that could reflect a comet-like dust tail trailing the planet; we present simulations of such a tail.